http://2012.igem.org/wiki/index.php?title=Special:Contributions&feed=atom&limit=20&target=Af.simbaqueba218&year=&month=2012.igem.org - User contributions [en]2021-01-19T19:29:35ZFrom 2012.igem.orgMediaWiki 1.16.0http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:05:04Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|600x600px|thumb|center]]<br />
Colombia iGEM Team - Grand Prize Winner<br />
[[File:Photo2.jpg|600x600px|thumb|center]]<br />
Colombia iGEM Team <br />
[[File:Photo3.jpg|600x600px|thumb|center]]<br />
Teams that advace to championship<br />
[[File:Photo4.jpg|600x600px|thumb|center]]<br />
Colombia iGEM Team - Best Model</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:02:53Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|600x600px|thumb|center]]<br />
[[File:Photo2.jpg|600x600px|thumb|center]]<br />
[[File:Photo3.jpg|600x600px|thumb|center]]<br />
[[File:Photo4.jpg|600x600px|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:02:24Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|1024x682px|thumb|center]]<br />
[[File:Photo2.jpg|1024x682px|thumb|center]]<br />
[[File:Photo3.jpg|1024x682px|thumb|center]]<br />
[[File:Photo4.jpg|1024x682px|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:02:02Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|1024x682|thumb|center]]<br />
[[File:Photo2.jpg|1024x682|thumb|center]]<br />
[[File:Photo3.jpg|1024x682|thumb|center]]<br />
[[File:Photo4.jpg|1024x682|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/File:Photo4.jpgFile:Photo4.jpg2012-10-27T04:01:18Z<p>Af.simbaqueba218: </p>
<hr />
<div></div>Af.simbaqueba218http://2012.igem.org/File:Photo3.jpgFile:Photo3.jpg2012-10-27T04:00:57Z<p>Af.simbaqueba218: </p>
<hr />
<div></div>Af.simbaqueba218http://2012.igem.org/File:Photo2.jpgFile:Photo2.jpg2012-10-27T04:00:38Z<p>Af.simbaqueba218: </p>
<hr />
<div></div>Af.simbaqueba218http://2012.igem.org/File:Photoone.jpgFile:Photoone.jpg2012-10-27T04:00:19Z<p>Af.simbaqueba218: </p>
<hr />
<div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:00:07Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|400px|thumb|center]]<br />
[[File:Photo2.jpg|400px|thumb|center]]<br />
[[File:Photo3.jpg|400px|thumb|center]]<br />
[[File:Photo4.jpg|400px|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T03:59:32Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photo1.jpg|400px|thumb|center]]<br />
[[File:Photo2.jpg|400px|thumb|center]]<br />
[[File:Photo3.jpg|400px|thumb|center]]<br />
[[File:Photo4.jpg|400px|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/StochasticTeam:Colombia/Modeling/Stochastic2012-10-27T03:51:31Z<p>Af.simbaqueba218: /* Stochastic Model */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== '''Stochastic Model''' ==<br />
<br />
<p align="justify"><br />
<br />
The previous sections showed how to know the mean behavior of the system for one cell, but this is just an average of the total proteins within the cell. All the biological systems are controlled by probability events. The cell is a huge space where there are a lot of small molecules. If we want a biological process to happen, two of these molecules have to find each other among millions in a huge pool. The differential equations do not take into account these uncontrollable events that can change the response dramatically. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
If we look only at one cell, it may not behave like we want and the system may not respond. Even worse, the probability of dying exist and our cell may die. But dealing with one cell is not real and we always work with hundreds of cells. Within this population, some cells may not behave as expected but others will and the average of cells would be able to respond to the presence of the pest.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
The stochastic algorithms are a way to model these probability events within a population. This simulation is made in order to confirm that the system dynamics are robust, consistent and show us if the response is still behaving like we want (taking probabilities into consideration). We use the Gillespie algorithm to develop our model. Here is a brief explanation of how it works: <br />
<br />
The complete method consists of eight steps.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::#Define the number of cells.<br />
::#Define the number of steps<br />
::#Define and name all the constants involved.<br />
::#Define creation and destruction events for each substance involved: The differential equations in this part have to be divided in two, the creation and the destruction expression. <br />
::#Apply [http://www.annualreviews.org/doi/pdf/10.1146/annurev.physchem.58.032806.104637 Gilliespie algorithm:] <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::• Calculate the sample space of the analyzed system: This is the sum of all the changes presented at specific time "t". <br />
<br />
[[File:sampspa.png|center|200x100pxpx]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::•Calculate time distribution that depends on a random number between 0 and 1.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:sampspa1.png|center|600x200pxpx]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::•Calculate which event occurs: The Gillespie algorithm does not consider simultaneous events, this is that in each time only one event occurs. In this case, the events are the creation or destruction of one protein. Each event has a probability of occurrence within the sample space between 0 and 1. To know which event occurs at the time "t+1", we take into account the random number use for the time distribution and look for the event that has this probability of occurrence . For example, if you see the sample space figure below, there are 5 possible events with their probability; if the random number is 0.4 then A is going to be destructed but if the random number is 0.55. then B will be created. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:sampspa2.png|center|500x300pxpx]]<br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::6. Take the outputs from the simulation and convert them into regular interval vectors.<br />
::7. Obtain the Gillespie function mean values.<br />
::8. Plot the obtained functions.<br />
<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/StochasticTeam:Colombia/Modeling/Stochastic2012-10-27T03:51:08Z<p>Af.simbaqueba218: /* Stochastic Model */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== '''Stochastic Model''' ==<br />
<br />
<p align="justify"><br />
<br />
The previous sections showed how to know the mean behavior of the system for one cell, but this is just an average of the total proteins within the cell. All the biological systems are controlled by probability events. The cell is a huge space where there are a lot of small molecules. If we want a biological process to happen, two of these molecules have to find each other among millions in a huge pool. The differential equations do not take into account these uncontrollable events that can change the response dramatically. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
If we look only at one cell, it may not behave like we want and the system may not respond. Even worse, the probability of dying exist and our cell may die. But dealing with one cell is not real and we always work with hundreds of cells. Within this population, some cells may not behave as expected but others will and the average of cells would be able to respond to the presence of the pest.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
The stochastic algorithms are a way to model these probability events within a population. This simulation is made in order to confirm that the system dynamics are robust, consistent and show us if the response is still behaving like we want (taking probabilities into consideration). We use the Gillespie algorithm to develop our model. Here is a brief explanation of how it works: <br />
<br />
The complete method consists of eight steps.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::#Define the number of cells.<br />
::#Define the number of steps<br />
::#Define and name all the constants involved.<br />
::#Define creation and destruction events for each substance involved: The differential equations in this part have to be divided in two, the creation and the destruction expression. <br />
::#Apply [[http://www.annualreviews.org/doi/pdf/10.1146/annurev.physchem.58.032806.104637 Gilliespie algorithm:]] <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::• Calculate the sample space of the analyzed system: This is the sum of all the changes presented at specific time "t". <br />
<br />
[[File:sampspa.png|center|200x100pxpx]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::•Calculate time distribution that depends on a random number between 0 and 1.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:sampspa1.png|center|600x200pxpx]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::•Calculate which event occurs: The Gillespie algorithm does not consider simultaneous events, this is that in each time only one event occurs. In this case, the events are the creation or destruction of one protein. Each event has a probability of occurrence within the sample space between 0 and 1. To know which event occurs at the time "t+1", we take into account the random number use for the time distribution and look for the event that has this probability of occurrence . For example, if you see the sample space figure below, there are 5 possible events with their probability; if the random number is 0.4 then A is going to be destructed but if the random number is 0.55. then B will be created. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:sampspa2.png|center|500x300pxpx]]<br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::6. Take the outputs from the simulation and convert them into regular interval vectors.<br />
::7. Obtain the Gillespie function mean values.<br />
::8. Plot the obtained functions.<br />
<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/AttributionsTeam:Colombia/Attributions2012-10-27T03:47:43Z<p>Af.simbaqueba218: /* Attributions */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
= '''Attributions''' =<br />
<br />
'''1.'''We would like to thank iGEM Colombia Team 2011*. Their original idea of sensing a fungal plant pathogen through a system of two transgenic bacterial variants is extended our the actual project, facilitating and improving key aspects of part design and modeling. Their experience contributed not only with concepts and strategies, but also by aiding to prevent and/or address several issues and pitfalls we have come across in the development of our work. We want to briefly mention some aspects that makes our project different from the 2011's. The idea to use genetically modified bacteria to detect pathogen molecules in an early stage of pathogen invasion is maintained this year, however, no parts from the previous project were used in this year project. iGEM Colombia team 2011 aimed to detect coffee rust fungus ''Hemileia vastatrix'' only. This year's team extends the idea of pathogen detection to detect also a bacterial pathogen, ''Ralstonia solanacearum'', which is a vascular pathogen of tomato ''Solanum lycopersicum'' and potato ''Solanum tuberosum'', as well as other crop plants. Another key feature introduced this year is the toxin-antitoxin modules which will be used to control the bacterial population density, prevent horizontal gene transfer and plasmid curing (in an antibiotic free strategy).<br />
<br />
The full list of team members can be found at http://2011.igem.org/Team:Colombia/Team.<br />
<br />
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<object width="700" height="600" align="center"> <br />
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</embed><br />
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<br />
'''2.'''The protocol for the persisters issolation we used is from the research work of Silvia Cañas (S. Cañas et al., manuscript in preparation, 2012). We thank Juan Manuel Pedraza, Silvia Restrepo and Sivia Cañas for lending us the protocol.<br />
<br />
'''3.'''We want to thank Lina Cabal for her help and advices to develop the layout of this page.<br />
<br />
'''4.'''Special thanks to Silvia Restrepo; her help, advices and accompaniment have been invaluable for this team.<br />
<br />
'''5.'''Special thanks to [http://medmicro.wisc.edu/people_faculty_profile.php?id=egruby&view=intro Dr. Edward Ruby] and [http://labs.medmicro.wisc.edu/ruby/members/ziegelhoffer/index.html Dr. Eva Ziegelhoffer] for gently providing the ''Aliivibrio fischeri'' ES114.<br />
<br />
'''6.'''Thanks also to [http://www.med.und.edu/microbiology/thomas-hill.cfm Dr. Thomas M. Hill] and [http://www.biology.neu.edu/faculty03/lewis03.html Dr. Kim Lewis] for providing us the ''E. coli'' strains: TH1269 and TH1268.<br />
<br />
'''7.''' We thank [http://lamfu/HOME/Home.html LAMFU] [http://cimic/Investigadores/jenny_dussan.htm CIMIC] and [http://biofisica.uniandes.edu.co/ Biophysics] labs for hosting our team!!! Thanks for the patience and collaboration!!<br />
<br />
'''8.''' For their collaboration with the organization of the Forum Research in Colombia: Obtaining Research Permits (Human Practice), Contracts for Access to Genetic Resources and Biological Collections, we want to thank:<br />
- Prof. Gonzalo Andrade, Universidad Nacional de Colombia.<br />
- Prof. Silvia Restrepo, Universidad de los Andes<br />
- Adriana Sierra, Public Relations, Universidad de los Andes.<br />
- Luisa Fernanda Bastidas, Public Relations, Universidad de los Andes.<br />
- Paola Pardo, Universidad de los Andes<br />
- Juan Gabriel Sutachan, Universidad de los Andes<br />
- Adriana Rosillo, Universidad de los Andes<br />
- Audiovisual Production – DTI, Universidad de los Andes<br />
- Facultad de Ciencias, Universidad de los Andes<br />
<br />
'''9.'''For their collaboration with the Social Schools and Coffee growers activities (Human Practice), we want to thank:<br />
- Federación Nacional de Cafeteros de Colombia<br />
- Dr. Fernando Gast, Federación Nacional de Cafeteros<br />
- Dr. Luis Francisco Useche Barbosa, Federación Nacional de Cafeteros<br />
- Mr. Leonardo Rojas, Federación Nacional de Cafeteros<br />
- Coffee Growers from Gualivá Region (Sasaima and Supatá)<br />
- Mrs. Patricia Méndez, Institución Educativa Rural San Bernardo, Sasaima.<br />
- Students and educational community of Institución Educativa Rural San Bernardo, Sasaima.<br />
<br />
'''10.'''Special thanks to Dr. Felipe Munoz Giraldo and all his research group to provide us computational resources (http://ingenieria.uniandes.edu.co/profesores/fmunoz/doku.php).<br />
<br />
'''11.'''Special thanks to Dr. Harold Castro and all his research group to provide us computational resources (http://sistemas.uniandes.edu.co/~hcastro/dokuwiki/doku.php).</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/AttributionsTeam:Colombia/Attributions2012-10-27T03:47:25Z<p>Af.simbaqueba218: /* Attributions */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
= '''Attributions''' =<br />
<br />
'''1.'''We would like to thank iGEM Colombia Team 2011*. Their original idea of sensing a fungal plant pathogen through a system of two transgenic bacterial variants is extended our the actual project, facilitating and improving key aspects of part design and modeling. Their experience contributed not only with concepts and strategies, but also by aiding to prevent and/or address several issues and pitfalls we have come across in the development of our work. We want to briefly mention some aspects that makes our project different from the 2011's. The idea to use genetically modified bacteria to detect pathogen molecules in an early stage of pathogen invasion is maintained this year, however, no parts from the previous project were used in this year project. iGEM Colombia team 2011 aimed to detect coffee rust fungus ''Hemileia vastatrix'' only. This year's team extends the idea of pathogen detection to detect also a bacterial pathogen, ''Ralstonia solanacearum'', which is a vascular pathogen of tomato ''Solanum lycopersicum'' and potato ''Solanum tuberosum'', as well as other crop plants. Another key feature introduced this year is the toxin-antitoxin modules which will be used to control the bacterial population density, prevent horizontal gene transfer and plasmid curing (in an antibiotic free strategy).<br />
<br />
The full list of team members can be found at http://2011.igem.org/Team:Colombia/Team.<br />
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'''2.'''The protocol for the persisters issolation we used is from the research work of Silvia Cañas (S. Cañas et al., manuscript in preparation, 2012). We thank Juan Manuel Pedraza, Silvia Restrepo and Sivia Cañas for lending us the protocol.<br />
<br />
'''3.'''We want to thank Lina Cabal for her help and advices to develop the layout of this page.<br />
<br />
'''4.'''Special thanks to Silvia Restrepo; her help, advices and accompaniment have been invaluable for this team.<br />
<br />
'''5.'''Special thanks to [http://medmicro.wisc.edu/people_faculty_profile.php?id=egruby&view=intro Dr. Edward Ruby] and [http://labs.medmicro.wisc.edu/ruby/members/ziegelhoffer/index.html Dr. Eva Ziegelhoffer] for gently providing the ''Aliivibrio fischeri'' ES114.<br />
<br />
'''6.'''Thanks also to [http://www.med.und.edu/microbiology/thomas-hill.cfm Dr. Thomas M. Hill] and [http://www.biology.neu.edu/faculty03/lewis03.html Dr. Kim Lewis] for providing us the ''E. coli'' strains: TH1269 and TH1268.<br />
<br />
'''7.''' We thank [http://lamfu/HOME/Home.html LAMFU] [http://cimic/Investigadores/jenny_dussan.htm CIMIC] and [http://biofisica.uniandes.edu.co/ Biophysics] labs for hosting our team!!! Thanks for the patience and collaboration!!<br />
<br />
'''8.''' For their collaboration with the organization of the Forum Research in Colombia: Obtaining Research Permits (Human Practice), Contracts for Access to Genetic Resources and Biological Collections, we want to thank:<br />
- Prof. Gonzalo Andrade, Universidad Nacional de Colombia.<br />
- Prof. Silvia Restrepo, Universidad de los Andes<br />
- Adriana Sierra, Public Relations, Universidad de los Andes.<br />
- Luisa Fernanda Bastidas, Public Relations, Universidad de los Andes.<br />
- Paola Pardo, Universidad de los Andes<br />
- Juan Gabriel Sutachan, Universidad de los Andes<br />
- Adriana Rosillo, Universidad de los Andes<br />
- Audiovisual Production – DTI, Universidad de los Andes<br />
- Facultad de Ciencias, Universidad de los Andes<br />
<br />
'''9.'''For their collaboration with the Social Schools and Coffee growers activities (Human Practice), we want to thank:<br />
- Federación Nacional de Cafeteros de Colombia<br />
- Dr. Fernando Gast, Federación Nacional de Cafeteros<br />
- Dr. Luis Francisco Useche Barbosa, Federación Nacional de Cafeteros<br />
- Mr. Leonardo Rojas, Federación Nacional de Cafeteros<br />
- Coffee Growers from Gualivá Region (Sasaima and Supatá)<br />
- Mrs. Patricia Méndez, Institución Educativa Rural San Bernardo, Sasaima.<br />
- Students and educational community of Institución Educativa Rural San Bernardo, Sasaima.<br />
<br />
'''10.'''Special thanks to Dr. Felipe Munoz Giraldo and all his research group to provide us computational resources (http://ingenieria.uniandes.edu.co/profesores/fmunoz/doku.php).<br />
<br />
'''10.'''Special thanks to Dr. Harold Castro and all his research group to provide us computational resources (http://sistemas.uniandes.edu.co/~hcastro/dokuwiki/doku.php).</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:40:44Z<p>Af.simbaqueba218: /* Mathematical Model Description */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|thumb|center|500px|Figure 1. Expected population dynamics ]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px|Table 1. Parameters and variables of this system ]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px|thumb|Figure 2. Toxin-Antitoxin levels as a function of chitin concentration ]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px|thumb|Figure 3. Salycilic acid level as a function of chitin concentration]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px|thumb|Figure 4. E. coli survival in coffee leaves]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:elcheck.jpg|center|700px|thumb|Figure 5. Model check results]]<br />
<br />
== Model Results ==<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:40:19Z<p>Af.simbaqueba218: /* Mathematical Model Description */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|thumb|center|Figure 1. Expected population dynamics ]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px|Table 1. Parameters and variables of this system ]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px|thumb|Figure 2. Toxin-Antitoxin levels as a function of chitin concentration ]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px|thumb|Figure 3. Salycilic acid level as a function of chitin concentration]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px|thumb|Figure 4. E. coli survival in coffee leaves]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:elcheck.jpg|center|700px|thumb|Figure 5. Model check results]]<br />
<br />
== Model Results ==<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:33:30Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx|Figure 10. Lux I - LuxR system substances]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx|Figure 11. Toxin/Antitoxin module substances]] [[File: rust5.png|center|thumb|450x450pxpx|Figure 12. CI and Salycilic Acid response]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:32:58Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx|Figure 10. Lux I - LuxR system substances]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx|Figure 11. Toxin/Antitoxin module substances]] [[File: rust5.png|center|450x450pxpx|Figure 12. Detection system substances]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:32:29Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx|Figure 10. Lux I - LuxR system substances]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx|Figure 11. Detection system substances]] [[File: rust5.png|center|450x450pxpx|Figure 12. Detection system substances]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:32:02Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx|Figure 10. Detection system substances]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx|Figure 11. Detection system substances]] [[File: rust5.png|center|450x450pxpx|Figure 12. Detection system substances]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:30:58Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218